Chapter 9 Risk and Return

1. Chapter 9 Risk and Return

2. Why Study Risk and Return? • Is there a way to invest in stocks to take advantage of the high returns while minimizing the risks? • Investing in portfolios enables investors to manage and control risk while receiving high returns. • A portfolio is a collection of financial assets

3. The General Relationship Between Risk and Return • Risk – The meaning in everyday language: The probability of losing some or all of the money invested • Understanding the risk-return relationship involves: • Define risk in a measurable way • Relate that measurement to a return

4. Portfolio Theory—Modern Thinking about Risk and Return • Portfolio theory defines investment risk in a measurable way and relates it to the expected level of return from an investment • Major impact on practical investing activities

5. The Return on an Investment • The rate of return allows an investment's return to be compared with other investments • One-Year Investments • The return on a debt investment is k = interest paid / loan amount • The return on a stock investment is k = [D1 + (P1 – P0)] / P0

6. The Expected Return • The expected return on stock is the return investors feel is most likely to occur based on current information • Anticipated return based on the dividends expected as well as the future expected price

7. The Required Return • The required return on a stock is the minimum rate at which investors will purchase or hold a stock based on their perceptions of its risk

8. Risk—A Preliminary Definition • A preliminary definition of investment risk is the probability that return will be less than expected • Feelings About Risk • Most people have negative feelings about bearing risk: Risk Aversion • Most people see a trade-off between risk and return • Higher risk investments must offer higher expected returns to be acceptable

9. Review of the Concept of a Random Variable • In statistics, a random variable is the outcome of a chance process and has a probability distribution • Discrete variables can take only specific variables • Continuous variables can take any value within a specified range

10. Review of the Concept of a Random Variable • The Mean or Expected Value • The most likely outcome for the random variable • For symmetrical probability distributions, the mean is the center of the distribution. • Statistically it is the weighted average of all possible outcomes

11. Review of the Concept of a Random Variable • Variance and Standard Deviation • Variability relates to how far a typical observation of the variable is likely to deviate from the mean • The standard deviation gives an indication of how far from the mean a typical observation is likely to fall

12. Review of the Concept of a Random Variable • Variance and Standard Deviation • Variance • Variance is the average squared deviation from the mean • Standard deviation

13. Concept Connection Example 9-1 Discrete Probability Distributions X P(X) 0 0.0625 The mean of this distribution is 2, since it is a symmetrical distribution. 1 0.2500 2 0.3750 3 0.2500 4 0.0625 1.0000 If you toss a coin four times, what is the chance of getting x heads?

14. Figure 9-1 Discrete Probability Distribution

15. Concept Connection Example 9-2 Calculating the Mean of a Discrete Distribution

16. Concept Connection Example 9-3 Variance and Standard Deviation

17. Review of the Concept of a Random Variable • The Coefficient of Variation • A relative measure of variation — the ratio of the standard deviation of a distribution to its mean CV = Standard Deviation  Mean

18. Review of the Concept of a Random Variable • Continuous Random Variable • Can take on any numerical value within some range • The probability of an actual outcome involves falling within a range of values rather than being an exact amount

19. Figure 9-2 Probability Distribution for a Continuous Random Variable

20. The Return on a Stock Investment as a Random Variable • Return is influenced by stock price and dividends • Return is a continuous random variable • The mean of the distribution of returns is the expected return • The variance and standard deviation show how likely an actual return will be some distance from the expected value

21. Figure 9-3 Probability Distribution of the Return on an Investment in Stock X

22. Figure 9-4 Probability Distributions With Large and Small Variances

23. Risk Redefined as Variability • In portfolio theory, risk is variability as measured by variance or standard deviation • A risky stock has a high probability of earning a return that differs significantly from the mean of the distribution • A low-risk stock is more likely to earn a return similar to the expected return • In practical terms risk is the probability that return will be less than expected

24. Figure 9-5 Investment Risk Viewed as Variability of Return Over Time Both stocks have the same expected return, the high risk stock has a greater variability in return over time.

25. Risk Aversion • Risk aversion means investors prefer lower risk when expected returns are equal • When expected returns are not equal the choice of investment depends on the investor's tolerance for risk

26. Figure 9-6 Risk Aversion

27. Concept Connection Example 9-4 Evaluating Stand-Alone Risk Harold will invest in one of two companies: Evanston Water Inc. (a public utility) AstroTech Corp. (a high-tech company). • Public utilities are low-risk - regulated monopolies • High tech firms are high-risk - new ideas can be very successful or fail completely Harold has made a discrete estimate of the probability distribution of returns for each stock:

28. Concept Connection Example 9-4 Evaluating Stand-Alone Risk Evaluate Harold's options in terms of the statistical concepts of risk and return.

29. Concept Connection Example 9-4 Evaluating Stand-Alone Risk First calculate the expected return for each stock. Next calculate the variance and standard deviation of the return on each stock:

30. Concept Connection Example 9-4 Evaluating Stand-Alone Risk

31. Concept Connection Example 9-4 Evaluating Stand-Alone Risk Finally, calculate the coefficient of variation for each stock’s return.

32. Example 9-4 Discussion • Which stock should Harold choose • Astro is better on expected return but Evanston wins on risk • Consider • Worst cases and Best cases • How variable is each return around its mean • Does a picture (next slide) help? • Which would you choose • Is it likely that Harold’s choice would be influenced by his age and/or wealth?

33. Concept Connection Example 9-4 Evaluating Stand-Alone Risk Continuous approximations of the two distributions are plotted as follows:

34. Decomposing Risk—Systematic and Unsystematic Risk • Movement in Return as Risk • Total up and down movement in a stock's return is the total risk inherent in the stock • Separate Movement/Risk into Two Parts • Market (systematic) risk • Business-specific (unsystematic) risk

35. Defining Market and Business-Specific Risk • Risk is Movement in Return • Components ofRisk • Market Risk • Movement caused by things that influence all stocks: political news, inflation, interest rates, war, etc. • Business-Specific Risk • Movement caused by things that influence particular firms and/or industries: labor unrest, weather, technology, key executives • Total Risk = Market Risk + Business-Specific Risk

36. Portfolios • A portfolio is the collection of investment assets held by an investor • Portfolios have their own risks and returns • A portfolio’s return is simply the weighted average of the returns of the stocks in it • Easy to calculate • A portfolio’s risk is the standard deviation of the probability distribution of its return • Depends on risks of stocks in portfolio, but... • Very complex and difficult to calculate/measure

37. Portfolios • Goal of the Investor/Portfolio Owner is to capture the high average returns of stocks while avoiding as much of their risk as possible • Done by constructing diversified portfolios • Investors are concerned only with how stocks impact portfolio performance, • not with stand-alone risk

38. Diversification—How Portfolio Risk Is Affected When Stocks Are Added • Diversification - adding different (diverse) stocks to a portfolio • Business-Specific Risk and Diversification • Business Specific risk: Random events • Good and Bad effects wash out in large portfolio • Business-Specific Risk is said to be “Diversified Away” in a well-diversified portfolio – • Portfolio Theory assumes it is gone

39. Diversifying to Reduce Market (Systematic) Risk • Market risk is caused by events that affect all stocks • Reduced but not eliminated by diversifying with stocks that do not move together • Not perfectly positively correlated with the market • Market risk in a portfolio depends on the timing of variations in individual returns (next slide)

40. Figure 9-7 Risk In and Out of a Portfolio

41. Portfolio Theory and the Small Investor • The Importance of Market Risk • Modern portfolio theory assumes business risk is diversified away • Large, diversified portfolio • For the small investor with a limited portfolio the theory’s results may not apply

42. Measuring Market RiskThe Concept of Beta • Market risk is crucial • It’s all that’s left because Business-Specific risk is diversified away • The theory needs a way to measure market risk for individual stocks • In the financial world, a stock’s “Beta” is a widely accepted measure of its risk • Beta measures the variation in a stock’s return that accompanies variation in the market's return

43. Measuring Market RiskThe Concept of Beta • Developing Beta • Determine the historical relationship between a stock's return and the return on the market • Regress stock’s return against return on an index such as the S&P 500 • Projecting Returns with Beta • Knowing a stock's Beta enables us to estimate changes in its return given changes in the market's return

44. Figure 9-8 The Determination of Beta

45. Concept Connection Example 9-6 Projecting Returns with Beta Conroy’s beta is 1.8. It’s stock returns 14%. The market is declining, and experts estimate the return on an average stock will fall by 4% from 12% to 8%. What is Conroy’s new return likely to be? Solution: Beta represents the past average change in Conroy’s return relative to changes in the market’s return. The new return can be estimated as kConroy= 14% - 7.2% = 6.8%

46. Measuring Market RiskThe Concept of Beta • Betas are developed from historical data • Not accurate if a fundamental change in the firm or business environment has occurred • Beta > 1.0 -- the stock moves more than the market • Beta < 1.0 -- the stock moves less than the market • Beta < 0 -- the stock moves against the market • Beta for a Portfolio • The weighted average of the betas of the individual stocks within the portfolio • Weighted by $ invested

47. Using Beta The Capital Asset Pricing Model CAPM) • CAPM attempts to explain how stock prices are set • CAPM's Approach • People won't invest in a stock unless its expected return is at least equal to their required return for that stock • CAPM attempts to quantify how required returns are determined • The stock’s value (price) is estimated based on CAPM’s required return for that stock

48. Using Beta The Capital Asset Pricing Model (CAPM) • Rates of Return, The Risk-Free Rate and Risk Premiums • The current return on the market is kM • The risk-free rate (kRF) – • no chance of receiving less than expected • Investing in any other asset is risky • Investors require a “risk premium” of additional return over kRF when there is risk

49. The CAPM’s Security Market Line (SML) • The SML proposes that required rates of return are determined by: • The Market Risk Premium is (kM – kRF) • The Risk Premium for Stock X • The beta for Stock X times the market risk premium • In the CAPM a stock’s risk premium is determined only by the stock's market risk as measured by its beta

50. Figure 9-9 The Security Market Line